Question

what can you conclude?
a. do not reject ( h_{0} ). there is sufficient evidence to conclude that ( p
eq0.40 ).
b. reject ( h_{0} ). there is sufficient evidence to conclude that ( p
eq0.40 ).
c. reject ( h_{0} ). there is sufficient evidence to conclude that ( p
eq0.40 ).
d. do not reject ( h_{0} ). there is insufficient evidence to conclude that ( p
eq0.40 ).
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Explanation:

Step1: Hypothesis testing basics

In hypothesis testing, if we do not reject \(H_0\) (the null hypothesis), it means we do not have enough evidence to support the alternative hypothesis. Here, the null hypothesis \(H_0\) would be related to \(p = 0.40\) (assuming a standard hypothesis setup for a proportion \(p\)).

Step2: Analyzing options

• Option A: “Do not reject \(H_0\). There is sufficient evidence to conclude that \(p

eq0.40\)” is incorrect. If we do not reject \(H_0\), we cannot say there is sufficient evidence for \(p
eq0.40\).

• Option B: “Reject \(H_0\). There is insufficient evidence to conclude that \(p

eq0.40\)” is wrong. Rejecting \(H_0\) would imply we have evidence for the alternative (\(p
eq0.40\)) not insufficient.

• Option C: “Reject \(H_0\). There is sufficient evidence to conclude that \(p

eq0.40\)” is incorrect as we are not told to reject \(H_0\) in the non - rejection scenario.

• Option D: “Do not reject \(H_0\). There is insufficient evidence to conclude that \(p

eq0.40\)” is correct. When we do not reject \(H_0\) (the null hypothesis, say \(H_0:p = 0.40\)), we do not have enough evidence to support the claim that \(p
eq0.40\) (the alternative hypothesis).

Answer:

D. Do not reject \(H_0\). There is insufficient evidence to conclude that \(p
eq0.40\)